For such systems, beyond two emitter antennas, the 1-rate space-time codes are non-orthogonal. This is the case for example with the Tirkkonen [6] and Jafarkhani [7] codes (the references cited in the present patent application are brought together in appendix 1).
The unavoidable non-orthogonality of these codes generally results in receivers that are complex to implement, needing to use maximum likelihood decoding or of a spherical type. The complexity of implementation of these algorithms increases exponentially as a function of the number of antennas and the number of states of the modulation. The techniques for the decoding of non-orthogonal space-time codes therefore have the major drawback, in reception systems, when 1-rate space-time codes are used, of being complex in their implementation. Prior non-iterative techniques are based on the maximum likelihood (ML) criterion.
Given the present state of technological progress, they are very complicated or even impossible to make, once the number of antennas or the number of states of the modulation increases since the complexity of implementation increases exponentially with the number of states of the trellis to be processed.
In the very recent past, iterative methods associating space-time codes have been published:
In [1], Tujkovic presents recursive trellis space-time turbo-codes. Reception is done iteratively (just as in the case of turbo-codes) in using MAP (Maximum A Posteriori) decoders;
In [2], S. Jayaweera studies the concatenation of a convolutive code with a 1-rate space-time code. The decoding is done iteratively by means of MAP algorithms;
And, in [3], A. Guillen and G. Caire analyse the performance of particular space-time codes, namely natural space-time codes and threaded space-time codes. They use an iterative interference canceller to separate the contributions made by the different emitter antennas;
In [4], Bauch uses an iterative system aimed at eliminating the inter-symbol interference introduced by the different channels. The elements used in each iteration bring MAP (Maximum a posteriori) type decoders into play.
These prior art iterative techniques can be applied to certain classes of space-time codes and most of them use non-linear equalizers (or detectors) that are also complicated to implement. The performance can be improved by concatenating a convolutive channel code (or even a turbo-code) with the space-time code at emission.
Boariu and M. Ionescu [5] present a class of minimal interference quasi-orthogonal space-time block codes. These codes can be decoded by an iterative interference cancellation method.
The technique presented in [5] is limited to four antennas with (4-state) QPSK modulation and a rate equal to 1. There are many approaches in which it cannot be implemented efficiently and in a way that it performs well, for example in a CDMA type of system. Furthermore, the adapted MRC (Maximum Ratio Combining) filter performs poorly with codes of types other than the one proposed.
Moreover, Boariu's approach assumes that the matrix used is of the same size as the space-time code.